Question

a balloon in the shape of a sphere has a volume v and surface area s if the balloon is blown up so as to have a volume of 8v without changing the spherical shape wat is new surface area is being blown up​

Answer 1

Answer:

the surface becomes 36 times the initial surface area.

Step-by-step explanation:

Volume of sphere is $V=\frac{4}{3}\pi r^3$

Surface area of sphere is $S=4\pi r^2$

Now, given that

Initial volume = v

Initial surface area = s

Final volume, v' = 8v

Final surface area = ?

Since, volume becomes 8 times the initial volume. Hence, we have

$V'=8\times\frac{4}{3}\pi r^3\\\\\frac{4}{3}\pi r'^3=8\times\frac{4}{3}\pi r^3\\\\r'^3=8r\\\\r'=2r$

Therefore, the final surface is

$s'=4\pi r'^2\\\\s'=4\pi(3r)^2\\\\s'=36\pi r^2\\\\s'=36s$

Therefore, the surface becomes 36 times the initial surface area.